Pseudoscalar heavy-quarkonium hadroproduction from nonrelativistic fragmentation at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>NLL</mml:mi> <mml:mo>/</mml:mo> <mml:msup> <mml:mrow> <mml:mi>NLO</mml:m

We investigate the inclusive hadroproduction of pseudoscalar heavy quarkonia, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>η</a:mi> <a:mi>c</a:mi> </a:msub> </a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>η</c:mi> <c:mi>b</c:mi> </c:msub> </c:math> mesons, in high-energy proton collisions. Our framework is based on the single-parton collinear fragmentation within a variable-flavor number scheme, tailored to describe the moderate to large transverse momentum regime. To this end, we construct a new set of collinear fragmentation functions, denoted as , which evolve via standard Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equations with a consistent treatment of flavor thresholds. Initial conditions for all parton-induced channels are computed using next-to-leading-order (NLO) nonrelativistic QCD. We perform our analysis within the next-to-leading <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mrow> <e:mi>logarithmic</e:mi> <e:mo>/</e:mo> <e:msup> <e:mrow> <e:mi>NLO</e:mi> </e:mrow> <e:mrow> <e:mo>+</e:mo> </e:mrow> </e:msup> </e:mrow> </e:math> hybrid factorization framework, employing the numerical interface together with the symbolic engine. These tools allow us to deliver predictions for high-energy observables sensitive to quarkonium final states at the 13 TeV LHC. To the best of our knowledge, the sets represent the first-ever release of collinear fragmentation functions for heavy quarkonia that consistently include all partonic channels within collinear factorization.